Sum and Product of Zeroes of Polynomial x^2 + x - 2

Finding the Zeroes of the Polynomial
To find the zeroes of the polynomial x^2 + x - 2, we need to solve the equation x^2 + x - 2 = 0. This can be done by factoring the quadratic equation or using the quadratic formula.

Factoring the Quadratic Equation
To factor x^2 + x - 2, we need to find two numbers that multiply to -2 and add up to 1 (coefficient of x). The numbers are 2 and -1. Therefore, the factored form of the quadratic equation is (x + 2)(x - 1) = 0.

Finding the Zeroes
Setting each factor to zero, we get x + 2 = 0 and x - 1 = 0. Solving these equations, we find the zeroes of the polynomial to be x = -2 and x = 1.

Sum of Zeroes
The sum of the zeroes of a quadratic polynomial is given by the formula -b/a, where a and b are the coefficients of x^2 and x, respectively. In this case, the sum of the zeroes is (-1)/1 = -1.

Product of Zeroes
The product of the zeroes of a quadratic polynomial is given by the constant term divided by the coefficient of x^2. In this case, the product of the zeroes is (-2)/1 = -2.

Conclusion
Therefore, the sum of the zeroes of the polynomial x^2 + x - 2 is -1, and the product of the zeroes is -2.